CE 167 Midterm #1
Fall 2000
Prof. C.W. Ibbs
Question #1
[15 Points]
The amount of $600 per year is to be paid into an account over each of the next 4 years.
The
nominal interest rate is 15% per year.
Determine the total amount the account will eventually
contain under the following conditions:
(a) Deposits are made at the beginning of the year with interest compounding yearly:
NFV = [$600 (F/A, 15%, 4)](1+i)
NFV = $600
)
1
(
1
)
1
(
i
i
i
n
+
−
+
NFV = $600
)
15
.
0
1
(
15
.
0
1
)
15
.
0
1
(
4
+
−
+
NFV = $344.45.43
(b) Deposits at the end of the year with interest compounding yearly:
NFV = [$600(F/A, 15%, 4)]
This is the same as the Part (a),
except you do not have to account
for the extra year of interest
NFV = $600
−
+
15
.
0
1
)
15
.
0
1
(
4
=
$2996.03
For Parts (a) & (b), 3 points were awarded for the correct usage of the formula, and 2 points
for the correct answer.
(c) $50 deposits are made at the end of each month with interest compounding monthly:
Since i = 15% is a nominal yearly rate
, you must find i
effective
:
i
effective
=
1
1
−
+
m
m
r
=
1
12
15
.
0
1
12
−
+
=
16.08%
i
effective
= 16.08% per year = 1.34% per month
This part was worth 1 point
A=$600
F=?
Because the equations are set up so that
payment are made at the end of the year
,
you have to account for the one extra
year’s worth of interest made by making
the deposit at the beginning of the year!
A=$600
F=?
0
1
2
3
0
1
2
3

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